Perfect matchings and derangements on graphs
Combinatorics
2019-10-14 v2
Abstract
We show that each perfect matching in a bipartite graph intersects at least half of the perfect matchings in . This result has equivalent formulations in terms of the permanent of the adjacency matrix of a graph, and in terms of derangements and permutations on graphs. We give several related results and open questions.
Cite
@article{arxiv.1906.05908,
title = {Perfect matchings and derangements on graphs},
author = {Matija Bucic and Pat Devlin and Mo Hendon and Dru Horne and Ben Lund},
journal= {arXiv preprint arXiv:1906.05908},
year = {2019}
}